The inner product of two $d$-dimensional vectors $A=[a_1,a_2,\dots,a_d]$ and $B=[b_1,b_2,\dots,b_d]$ is the sum of the products of their corresponding components, defined as:

\begin{equation} \langle A, B\rangle = \sum_{i = 1}^{d} a_i b_i = a_1 b_1 + a_2 b_2 + \dots + a_d b_d \end{equation}

Given $n$ vectors $x_1, x_2, \dots, x_n$ in $d$-dimensional space, Xiao Miaomiao wants to know if there exist two vectors whose inner product is a multiple of $k$. Please help her solve this problem.

Input

The first line contains three positive integers $n, d, k$, representing the number of vectors, the dimension, and the multiple to be checked, respectively.

The next $n$ lines each contain $d$ non-negative integers, where the $j$-th integer in the $i$-th line represents the $j$-th dimension weight $x_{i,j}$ of vector $x_i$.

Output

Output two integers separated by a space.

If there exist two vectors $x_p$ and $x_q$ such that their inner product is an integer multiple of $k$, output the indices $p$ and $q$ (where $p < q$). If there are multiple such pairs, output any one of them.

If no such pair of vectors exists, output two $-1$s.

Examples

Input 1

3 5 2
1 0 1 0 1
1 1 0 1 0
0 1 0 1 1

Output 1

2 3

Note 1

$\langle x_1, x_2 \rangle = 1$, $\langle x_1, x_3 \rangle = 1$, $\langle x_2, x_3 \rangle = 2$.

Input 2

(See provided files)

Output 2

(See provided files)

Input 3

(See provided files)

Output 3

(See provided files)

Constraints